Methods and systems for optimizing data accesses

ABSTRACT

A method for optimizing data types includes the step of generating a data structure providing access to at least one data element, the data structure associated with a first representation of the at least one data element. A user is provided with a plurality of data types for accessing the at least one data element. A request for access to the at least one data element is received, the request including at least one of the plurality of data types. The request is responded to with a second representation of the at least one data element, the second representation generated responsive to the at least one of the plurality of data types.

FIELD OF THE INVENTION

The present invention relates to methods and systems for optimizing dataaccess. In particular, the present invention relates to methods andsystems for generating data structures providing optimized access todata elements.

BACKGROUND OF THE INVENTION

A new generation of massively parallel processors, including graphicsprocessing units (GPUs), the IBM Cell BE processor, and other multi-coreor vector processors, can offer faster computation than traditionalprocessors by an order of magnitude. Achieving the potential performanceof these processors typically requires a detailed understanding ofprocessor hardware and memory architectures as well as of sophisticatedparallel programming techniques. For example, typically programmingapplications for graphical processing units may require programmers tolearn a large number of graphics concepts as well as understandingdifferent optimizations required to achieve optimum performance in anenvironment in which the cache, memory and execution architectures maydiffer significantly from that of traditional processing units.Additionally, parallel programming itself is not intuitive for manyprogrammers, as it requires techniques and algorithms that are notrequired for traditional serial programming and introduces numerous newdevelopment and debugging challenges.

BRIEF SUMMARY OF THE INVENTION

Because of the memory, communication, processing, and architecturalfeatures of massively parallel processors, new development approachesand programming systems may be used to improve the level of performanceachievable with these processors. One system that may be used to improvea performance level includes a set of data types and operations thatprovide a user with meaningful and useful primitives and allowshigh-performance implementations of the user's programs. In one aspect,systems and methods for optimizing data accesses provide users withthree abstractions: an abstraction of data types having optimizedassignment semantics, an abstraction of data elements, and anabstraction of optimized methods for generating the data types andoperating on the data elements.

In one aspect, a method for optimizing data access includes the step ofgenerating a data structure providing access to at least one dataelement, the data structure associated with a first representation ofthe at least one data element. A user is provided with a plurality ofdata types for accessing the at least one data element. A request foraccess to the at least one data element is received, the requestincluding at least one of the plurality of data types. The request isresponded to with a second representation of the at least one dataelement, the second representation generated responsive to the at leastone of the plurality of data types.

In one embodiment, the first representation stores a copy of the atleast one data element. In another embodiment, each of the data types inthe plurality of data types are associated with the data structureproviding access to the at least one data element. In still anotherembodiment, a data type in the plurality of data types has by-valuesemantics. In still even another embodiment, a data type in theplurality of data types has by-reference semantics. In yet anotherembodiment, a data type in the plurality of data types providingdereferenced access to the at least one data element.

In one embodiment, a data type providing access to the secondrepresentation is identified, the data type having an assignmentsemantic selected responsive to an analysis of the at least one of theplurality of data types included in the request. In another embodiment,the request for access to the at least one data element is responded towith an optimized representation of the at least one data element, theoptimized representation generated responsive to an analysis of ahardware component on which the at least one data element resides. Instill another embodiment, the request for access to the at least onedata element is responded to with an optimized representation of the atleast one data element, the optimized representation generatedresponsive to an analysis of the at least one data element. In stilleven another embodiment, the request for access to the at least one dataelement is responded to with an optimized representation of the at leastone data element, the optimized representation generated responsive toan analysis of a memory layout of the at least one data element.

In another aspect, a system for optimizing data access includes a datastructure providing access to at least one data element, a firstrepresentation of the at least one data element, a plurality of datatypes for accessing the at least one data element, and a secondrepresentation of the at least one data element, the representationgenerated responsive to at least one of the plurality of data types.

BRIEF DESCRIPTION OF THE DRAWINGS

The foregoing and other objects, aspects, features, and advantages ofthe invention will become more apparent and better understood byreferring to the following description taken in conjunction with theaccompanying drawings, in which:

FIGS. 1A-1C are block diagrams depicting an embodiment of a computeruseful in connection with the methods and systems described herein;

FIG. 2 is a block diagram depicting one embodiment of a system foroptimizing data access;

FIG. 3 is a flow diagram depicting one embodiment of the steps taken ina method for optimizing data types; and

FIG. 4 is a block diagram depicting one embodiment of a data structureproviding access to a data element, a plurality of data types, and arepresentation of the data element.

DETAILED DESCRIPTION OF THE INVENTION

FIG. 1A depicts a block diagram of a computing device 100 useful forpracticing an embodiment of a method for optimizing data access. Asshown in FIG. 1, each computing device 100 includes one or more centralprocessing units 121, and one or more main memory units 122. As shown inFIG. 1, a computing device 100 may include a visual display device 124,a keyboard 126 and/or a pointing device 127, such as a mouse. Acomputing device may also include installation devices, which may or maynot be the same as the central processing units.

The central processing unit 121 is any logic circuitry that responds toand processes instructions fetched from the main memory unit 122. Inmany embodiments, the central processing unit is provided by amicroprocessor unit, such as: those manufactured by Intel Corporation ofMountain View, Calif.; those manufactured by Motorola Corporation ofSchaumburg, Ill.; those manufactured by Transmeta Corporation of SantaClara, Calif.; those manufactured by International Business Machines ofWhite Plains, N.Y.; those manufactured by Sun Microsystems Inc. ofMountain View, Calif.; or those manufactured by Advanced Micro Devicesof Sunnyvale, Calif. The computing device 100 may be based on any ofthese processors, or any other processor capable of operating asdescribed herein.

As shown in FIG. 1B, the computing device 100 may comprise multipleprocessors and may provide functionality for simultaneous execution ofinstructions or for simultaneous execution of one instruction on morethan one piece of data. In some embodiments, the computing device 100may comprise a parallel processor with one or more cores. In one ofthese embodiments, the computing device 100 is a shared memory paralleldevice, with multiple processors and/or multiple processor cores,accessing all available memory as a single global address space. Inanother of these embodiments, the computing device 100 is a distributedmemory parallel device with multiple processors each accessing localmemory only. In still another of these embodiments, the computing device100 has both some memory which is shared and some memory which can onlybe accessed by particular processors or subsets of processors. In stilleven another of these embodiments, the computing device 100, such as amulticore microprocessor, combines two or more independent processorsinto a single package, often a single integrated circuit (IC). In yetanother of these embodiments, the computing device 100 includes a chiphaving a CELL BROADBAND ENGINE architecture and including a Powerprocessor element and a plurality of synergistic processing elements,the Power processor element and the plurality of synergistic processingelements linked together by an internal high speed bus, which may bereferred to as an element interconnect bus.

In some embodiments, the processors provide functionality for executionof a single instruction simultaneously on multiple pieces of data(SIMD). In other embodiments, the processors provide functionality forexecution of multiple instructions simultaneously on multiple pieces ofdata (MIMD). In still other embodiments, the processor may use anycombination of SIMD and MIMD cores in a single device.

In some embodiments, the computing device 100 may comprise a graphicsprocessing unit. In one of these embodiments, depicted in FIG. 1C, thecomputing device 100 includes at least one central processing unit 121and at least one graphics processing unit. In another of theseembodiments, the computing device 100 includes at least one parallelprocessing unit and at least one graphics processing unit. In stillanother of these embodiments, the computing device 100 includes aplurlality of processing units of any type, one of the plurality ofprocessing units comprising a graphics processing unit.

The computing device 100 may include a network interface 118 tointerface to a Local Area Network (LAN), Wide Area Network (WAN) or theInternet through a variety of connections including, but not limited to,standard telephone lines, LAN or WAN links (e.g., 802.11, T1, T3, 56 kb,X.25), broadband connections (e.g., ISDN, Frame Relay, ATM), wirelessconnections, or some combination of any or all of the above. The networkinterface 118 may comprise a built-in network adapter, network interfacecard, PCMCIA network card, card bus network adapter, wireless networkadapter, USB network adapter, modem or any other device suitable forinterfacing the computing device 100 to any type of network capable ofcommunication and performing the operations described herein.

A wide variety of I/O devices may be present in the computing device100. Input devices include keyboards, mice, trackpads, trackballs,microphones, and drawing tablets. Output devices include video displays,speakers, inkjet printers, laser printers, and dye-sublimation printers.The I/O devices may be controlled by an I/O controller 123 as shown inFIG. 1. The I/O controller may control one or more I/O devices such as akeyboard 126 and a pointing device 127, e.g., a mouse or optical pen.Furthermore, an I/O device may also provide storage and/or aninstallation medium 116 for the computing device 100. In still otherembodiments, the computing device 100 may provide USB connections toreceive handheld USB storage devices such as the USB Flash Drive line ofdevices manufactured by Twintech Industry, Inc. of Los Alamitos, Calif.

In some embodiments, the computing device 100 may comprise or beconnected to multiple display devices 124 a-124 n, which each may be ofthe same or different type and/or form. As such, any of the I/O devicesand/or the I/O controller 123 may comprise any type and/or form ofsuitable hardware, software, or combination of hardware and software tosupport, enable or provide for the connection and use of multipledisplay devices 124 a-124 n by the computing device 100.

In further embodiments, an I/O device may be a bridge between the systembus 150 and an external communication bus, such as a USB bus, an AppleDesktop Bus, an RS-232 serial connection, a SCSI bus, a FireWire bus, aFireWire 800 bus, an Ethernet bus, an AppleTalk bus, a Gigabit Ethernetbus, an Asynchronous Transfer Mode bus, a HIPPI bus, a Super HIPPI bus,a SerialPlus bus, a SCI/LAMP bus, a FibreChannel bus, an Infibandinterconnect fabric, a Myrinet interconnect fabric, or a Serial Attachedsmall computer system interface bus.

A computing device 100 of the sort depicted in FIG. 1 typically operatesunder the control of operating systems, which control scheduling oftasks and access to system resources. The computing device 100 can berunning any operating system such as any of the versions of theMICROSOFT WINDOWS operating systems, the different releases of the Unixand Linux operating systems, any version of the MAC OS for Macintoshcomputers, any embedded operating system, any real-time operatingsystem, any open source operating system, any proprietary operatingsystem, any operating systems for mobile computing devices, or any otheroperating system capable of running on the computing device andperforming the operations described herein. Typical operating systemsinclude: WINDOWS 3.x, WINDOWS 95, WINDOWS 98, WINDOWS 2000, WINDOWS NT3.51, WINDOWS NT 4.0, WINDOWS CE, WINDOWS XP, and WINDOWS VISTA all ofwhich are manufactured by Microsoft Corporation of Redmond, Wash.; MACOS, manufactured by Apple Computer of Cupertino, Calif.; OS/2,manufactured by International Business Machines of Armonk, N.Y.; SolarisOperating System, manufactured by Sun Microsystems, Inc. of Santa Clara,Calif.; and Linux, a freely-available operating system distributed byCaldera Corp. of Salt Lake City, Utah, or any type and/or form of a Unixoperating system, among others. In some embodiments, the computingdevice 100 operates under the control of an operating system supportingparallel processing. In one of these embodiments, the operating systemprovides functionality for managing shared resources, scheduling, andcoordination of processing performed by multiple processors. In otherembodiments, the computing device 100 operates under a minimal BasicInput/Output System but has the ability to load a standard operatingsystem, such as WINDOWS CE or other WINDOWS operating system.

The computing device 100 can be any workstation, desktop computer,laptop or notebook computer, server, handheld computer, mobiletelephone, game console, any other computer, or other form of computingor telecommunications device that is capable of communication and thathas sufficient processor power and memory capacity to perform theoperations described herein.

Referring now to FIG. 2, a block diagram depicts one embodiment of asystem for optimizing data accesses. In brief overview, the systemincludes a plurality of data types 202 a-202 n, a data structure 204, afirst representation 206, at least one data element 210, an optimizationcomponent 212, a second representation 214, a program 216, an optimizedprogram 218, and a runtime component 220. The data structure 204provides access to at least one data element 210. The firstrepresentation 206 of the at least one data element is associated withthe data structure 204. The plurality of data types 202 provide accessto the at least one data element 210. The second representation 214 ofthe at least one data element 210 is generated responsive to at leastone of the plurality of data types 202.

A user is provided with a plurality of data types 202 for accessing theat least one data element. In one embodiment, the user generates aprogram—a collection of computations—using at least one of the pluralityof data types 202 to access the at least one data element 210. Inanother embodiment, the program includes code for reading, writing,modifying or otherwise operating on the at least one data element 210.In still another embodiment, the system for optimizing data accessesreceives the program.

In one embodiment, an optimization component 212 includes a codegenerator that generates an optimized schedule of operations and selectsa data layout from a plurality of data layout options. In anotherembodiment, an optimization takes place when a program 216 is combined,either statically or dynamically, with an actual source of data througha particular access pattern. Requests to combine a program 216 with asource of data and execute it may be dynamically specified by a user.

In some embodiments, the optimization component 212 analyzes theprogram. In one of these embodiments, the optimization component 212analyzes a data structure 204 associated with the at least one of theplurality of data types 202 and providing an internal representation ofthe at least one of the plurality of data types 202. In another of theseembodiments, the optimization component 212 analyzes a plurality of datatypes used in the program. In still another of these embodiments, theoptimization component 212 analyzes the data element 210. In still evenanother of these embodiments, the optimization component 212 analyzes atarget processing unit that will perform the requested operations. Inyet another of these embodiments, the optimization component 212generates an optimized representation of the at least one data elementfor use in performing the requested operation on the at least one dataelement 210, the representation optimized responsive to at least oneanalysis performed by the optimization component 212. In furtherembodiments, the optimization component 212 generates an optimizedrepresentation of the at least one data type for use in performing therequested operation on the at least one data element 210, therepresentation optimized responsive to at least one analysis performedby the optimization component 212.

Referring now to FIG. 3, and in conjunction with FIG. 2, a flow diagramdepicts one embodiment of the steps taken in a method for optimizingdata types. In brief overview, a data structure providing access to atleast one data element is generated, the data structure associated witha first representation of the at least one data element (step 302). Auser is provided with a plurality of data types for accessing the atleast one data element (step 304). A request for access to the at leastone data element is received, the request including at least one of theplurality of data types (step 306). The request is responded to with asecond representation of the at least one data element, the secondrepresentation generated responsive to the at least one of the pluralityof data types (step 308).

A data structure 204 providing access to at least one data element 210is generated, the data structure associated with a first representation206 of the at least one data element 210 (step 302). In one embodiment,the data structure 204 is a node. In another embodiment, the datastructure 204 is referred to as an array node. In still anotherembodiment, the data structure 204 provides access to the at least onedata element 210 by providing access to the plurality of data types 202.In yet another embodiment, the data structure 204 provides access to theat least one data element 210 by providing access to the firstrepresentation 206.

In one embodiment, the first representation 206 of the at least one dataelement 210 is referred to as an array source 206. In anotherembodiment, an array node 204 is associated with an array source 206. Instill another embodiment, a plurality of array nodes 204 are associatedwith an array source 206. In still even another embodiment, an arraynode 204 is referred to as an owner of its associated array source 206.In yet another embodiment, an array source 206 provides a representationof at least one element exposed through an array node 204. In someembodiments, elements of an array node may include any form of data,including fixed-size data, such as sequences of basic types includingfloating point numbers and integers or any other bit pattern. In otherembodiments, elements may also include recursive containers, includingsequences of different types and other arrays. In one of theseembodiments, the elements may be of variable size.

In some embodiments, the first representation 206 identifies a methodfor generating the at least one data element 210. In one of theseembodiments, an array source 206 specifies how to generate an element inan array node 204 associated with the array source 206. In another ofthese embodiments, a method for generating the at least one data element210 generates the element given its position in an array (for example,so that the array appears to contain a sequence of natural numbers), orany other function of such positions, for example, a sequence ofpseudo-random numbers or quasi-random numbers generated by a hashfunction of position. In still another of these embodiments, agenerating function may also generate a constant.

In other embodiments, the first representation 206 identifies a statusof an initialization process of the data structure 204 providing accessto the at least one data element 210. In one of these embodiments, aninvalid, or null, array source 206 indicates that an associated arraynode 204 is uninitialized. In another of these embodiments, an invalid,or null, array source 206 indicates that an associated array node 204 ispartially initialized. In still another of these embodiments, an arraysource 206 generated by default may be a null source 206. In still evenanother of these embodiments, an array node 204 generated by default maybe associated with a null source 206. In yet another of theseembodiments, storage for an array source 206 is only allocated as anarray is accessed. For example, an array may be stored as a set oftiles, with uninitialized tiles represented with null sources. Physicalstorage for tiles only needs to be allocated when these locations arewritten to, and when read such uninitialized array nodes can generatearbitrary data or an error can be signal. In further embodiments,uninitialized array sources 206 represent the state of the array,indicating that the actual storage has not been allocated or written.

In some embodiments, the first representation 206 stores a constant. Inother embodiments, the first representation 206 stores data of a fixedsize. In still other embodiments, the data includes the at least onedata element 210 provided by the associated data structure 204. In stilleven other embodiments, the at least one data element 210 comprises datadistributed over multiple storage locations. In yet other embodiments,the first representation 206 stores data of variable size.

In one embodiment, the first representation 206 includes an array ofindices. In another embodiment, the first representation 206 includes arepresentation of an array of indices. In still another embodiment, thefirst representation 206 includes a representation of an arrayrepresenting an index to a second array. In still even anotherembodiment, the first representation 206 includes a pointer to an arrayindexing the at least one data element 210. In yet another embodiment,the first representation 206 includes a pointer to an array indexing asecond array. In some embodiments, the first representation 206 providesan index for a second array node 202 b′. In other embodiments, the firstrepresentation 206 includes an array of indices that is conceptuallyunbounded. In one of these embodiments, the array of indices iscomputed, rather than stored in memory.

In some embodiments, a transformation is applied to an array indexingthe at least one data element 210. In one of these embodiments, the atleast one data element 210 is a second array. In one embodiment, toaccess certain elements of an array, an affine transformation is appliedto an index of the array (for example, by multiplying a data element inthe index by two and adding one to access the odd elements of thearray). In another of these embodiments, non-affine transformations areapplied to array indices. In still another of these embodiments, thearray indices are multidimensional. In still even another of theseembodiments, a multidimensional affine transformation is represented asa matrix is applied using a matrix-vector multiplication tomultidimensional indices represented as a vector extended with ahomogeneous coordinate. In yet another of these embodiments, non-affinemultidimensional transformations are applied to an index. In furtherembodiments, a multidimensional affine transformation is represented asa matrix and an offset vector and applied using a matrix-vectormultiplication and a vector addition to multidimensional indicesrepresented as a vector.

In other embodiments, a data type 202 b in the plurality of data types202 is associated with an identification of a transformation. In one ofthese embodiments, the array node 202 b stores the transformation. Instill other embodiments, an optimized representation is generated usingthe transformation. In one of these embodiments, a request for anoperation on a data element 210 includes a request for the applicationof a transformation to the data element 210. In yet other embodiments,indirect transformations are applied to a data element 210 through proxysources. In further embodiments, the transformations will be taken intoaccount during certain operations on elements of the array. In one ofthese embodiments, the result of performing the transformation is storedand the transformation becomes an identity.

In one embodiment, the first representation 206 stores a copy of the atleast one data element 210. In some embodiments, the firstrepresentation 206 stores a procedurally-generated version of the atleast one data element 210. In one of these embodiments, the firstrepresentation 206 of the at least one data element 210 includes arepresentation of a procedurally-generated sequence of numbers. Inanother of these embodiments, the first representation 206 stores aprocedurally-generated copy of the at least one data element 210, thecopy including at least one pseudo-random number. In still another ofthese embodiments, the first representation 206 stores aprocedurally-generated copy of the at least one data element 210, thecopy including at least one constant.

In one embodiment, the first representation 206 is stored remotely fromthe at least one data element 210. In another embodiment, the firstrepresentation 206 is stored on a disk storing the at least one dataelement 210. In another embodiment, the first representation 206 of theat least one data element 210 stores a representation of the at leastone data element 210, the at least one data element 210 stored on a diskidentified by the first representation 206.

In some embodiments, the first representation 206 represents a copy ofat least one data element 210 provided by a second array node 202 b′. Inone of these embodiments, the first representation 206 is associatedwith a second data structure 204′ providing access to a second dataelement 210′. In another of these embodiments, the first representation206 includes an identification of a representation of a second dataelement 204′. In still another of these embodiments, the firstrepresentation 206 stores a copy of a second data element 210′, thesecond data element 210′ also associated with a second representation206′. In still even another of these embodiments, the firstrepresentation 206 stores a copy of a second data element 210′ providedby a second data structure 204′.

In some embodiments, an array source 206 representing a copy of a dataelement associated with a second array node 204′ is referred to as aproxy source 206. In one of these embodiments, a proxy source representsmultiple layers of access patterns. In another of these embodiments,requests for certain operations on the at least one data element 210require converting a proxy source 206 associated with the at least onedata element 210—and, in some embodiments, storing a reference to the atleast one data element 210—to an array source 206 storing a copy of theat least one data element 210.

A user is provided with a plurality of data types for accessing the atleast one data element (step 304). In some embodiments, a data type 202a in the plurality of data types 202 has by-value semantics for copyingand when one array is assigned to another, it is as if the data wascopied, and all prior data in the array is destroyed. In some of theseembodiments, the new value of the array may have a new size. In othersof these embodiments, the data is copied to the target array.

In one of these embodiments, the data type 202 a is referred to as anarray. In another of these embodiments, the data type 202 a represents avariable-size, multidimensional set of indexed homogeneous data. Instill another of these embodiments, the data type 202 a represents avariable-size, multidimensional set of indexed data of a user-definedinhomogeneous type. In another of these embodiments, the data type 202 astores a copy of the at least one data element. In still even another ofthese embodiments, the data type 202 a is a container for a plurality ofdata elements 210. In yet another of these embodiments, the array 202 amimics a C++ container. In other embodiments, an array 202 a has by-copyassignment semantics. In one of these embodiments, an operationperforming a copy for array 202 a may be optimized to defer the copy. Inanother of these embodiments, an operation performing a copy for array202 a may be optimized to minimize the amount of copying required by thearray 202 a.

In other embodiments, a data type 202 b in the plurality of data types202 has by-reference semantics, and when one array is assigned toanother, the array assigned to will refer to the storage location of theoriginal array; the assignment is that of a pointer to the originaldata. In one of these embodiments, the data type 202 b is referred to asan accessor 202 b. In another of these embodiments, an accessor 202 brepresents a subset of a data element 210 represented by an array 202 a.In still another of these embodiments, an accessor 202 b stores a subsetof a data element 210. In still even another of these embodiments, theaccessor 202 b mimics groups of C++ iterators.

In still other embodiments, a data type 202 c in the plurality of datatypes 202 provides dereferenced access to the at least one data element210. In one of these embodiments, the data type 202 c is referred to asa chunk. In another of these embodiments, the chunk 202 c is adereferenced accessor 202 b. In still another of these embodiments, anoperator is provided for dereferencing an accessor 202 b to generate achunk 202 c. In some embodiments, the chunk 202 c has content-modifyingassignment semantics. In one of these embodiments, content-modifyingsemantics modify a storage location in-place and are similar to by-valueassignments, except that not all of the data is necessarily modified.

In some embodiments, each data type in the plurality of data types 202is associated with the same data structure 204. In one of theseembodiments, each data type in the plurality of data types 202 isassociated with the same first representation 206. In other embodiments,each data type in the plurality of data types 202 is associated with aseparate data structure 204. In one of these embodiments, each data typein the plurality of data types 202 is referred to as an owner of itsdata structure 204. In another of these embodiments, each data structure204 is associated with a separate first representation 206. In stillanother of these embodiments, each data structure 204 is associated witha single first representation 206.

In one embodiment, a plurality of array nodes 204 provides access to atleast one data element 210, each array node 204 in the plurality ofarray nodes 204 associated with a data type in the plurality of datatypes 202. In another embodiment, the plurality of array nodes 204 is aplurality of nodes in a closed, doubly-linked list, which may bereferred to as a ring. In still another embodiment, the plurality ofarray nodes 204 is stored in an alternative data type supportingequivalent abstract operations as a doubly-linked list.

In other embodiments, the data structure 204 providing access to the atleast one data element 210 is associated with the plurality of datatypes 202. In one of these embodiments, the data structure 204 providingaccess to the at least one data element 210 provides the user with theplurality of data types 202. In another of these embodiments, an arraynode 204 is associated with an array 202 a, an accessor 202 b and achunk 202 c provided to a user. In still another of these embodiments,an array node 204 provides a representation of an array 202 a. In yetanother of these embodiments, array node 204 provides a representationof an accessor 202 b. In still other embodiments, an array 202 a, anaccessor 202 b, and a chunk 202 c are associated with a single arraynode 204, which provides a common representation for the array 202 a,the accessor 202 b, and the chunk 202 c.

In some embodiments, a data type in the plurality of data types 202 isassociated with an identification of an affine transformation. In one ofthese embodiments, the data type 202 n stores a copy of the at least onedata element 210 to which an affine transformation is applied. In otherembodiments, a data type in the plurality of data types 202 isassociated with an identification of a non-affine transformation. In oneof these embodiments, the data type 202 n stores a copy of the at leastone data element 210 to which a non-affine transformation is applied.

In one embodiment, a data type in the plurality of data types 202 isassociated with an identification of a size of a subset of the at leastone data element 210. In another embodiment, a data type in theplurality of data types 202 is associated with an identification of aregion of a subset of the at least one data element 210. In stillanother embodiment, a data type in the plurality of data types 202 isassociated with an identification of a region of a subset of the atleast one data element 210, the region specified by a user. In stilleven another embodiment, a data type in the plurality of data types 202is associated with an identification of a stride of an array. In yetanother embodiment, a data type in the plurality of data types isassociated with an identification of an offset within an array.

In some embodiments, a data type 202 is associated with anidentification of a region of a subset of the at least one data element210, with a stride of an array provided by the data type, and with anoffset within the array. In one of these embodiments, the identificationof the region, the identification of the stride, and the identificationof the offset are referred to as an access pattern. In another of theseembodiments, the data type 202 has an access pattern allowing a user toaccess an arbitrary regular pattern of an array. In still another ofthese embodiments, the access pattern is associated with amultidimensional affine transformation. In still even another of theseembodiments, the data type 202 associated with the access pattern is anaccessor 202 b. In other embodiments, an array node 204 associated witha data type in the plurality of data types 202 stores an access pattern.In one of these embodiments, the array node 204 is associated with anarray 202 a. In another of these embodiments, the array node 204 isassociated with a chunk 202 c. In still another of these embodiments,the array node 204 is associated with an accessor 202 b. In yet anotherof these embodiments, multiple levels of nested access patterns arerepresented using a proxy source 206.

In one embodiment, a data type in the plurality of data types 202 isassociated with an identification of a boundary condition. In someembodiments, a boundary condition includes, but is not limited to, oneof the following: undefined, safe undefined, checked undefined,constant, repeat, clamp. In one of these embodiments, an undefinedboundary condition specifies that writes outside the boundary are unsafeand may corrupt the execution environment of the program and reads willreturn undefined results. In another of these embodiments, a safeundefined boundary condition is similar to the undefined boundarycondition; however, writes outside the boundary will have no effect andwill not corrupt the execution environment of the program. In stillanother of these embodiments, the checked undefined boundary conditionis similar to the safe undefined boundary condition; however, attemptsto read or write outside the boundaries will result in an error beingflagged. In still even another of these embodiments, the constantboundary condition is similar to the safe undefined boundary conditionfor reads; however, the condition returns a user-specified constant forreads outside the boundary. In still another embodiment, the repeatboundary condition toroidially wraps all accesses outside the boundaryto accesses inside the boundary. In yet another embodiment, the clampboundary condition maps all accesses outside the boundary to the closestpoint on the boundary.

In one embodiment, a boundary is an infinite area outside of a definedsize of an array 202 a. In another embodiment, a data type in theplurality of data types 202 is associated with an identification of anaction taken when a request is received to read or write a data elementoutside of a boundary of an array 202 a. In still another embodiment,the identification may be referred to as a boundary mode. In someembodiments, data supporting a boundary condition is generated andmaintained. In one of these embodiments, for example, a boundaryconstant is generated and used to return an appropriate value duringreads outside of the boundary.

A request for access to the at least one data element is received, therequest including at least one of the plurality of data types (step306). In one embodiment, the request is included in a program 216. Inanother embodiment, the request is for computation of an operation onthe at least one data element.

In one embodiment, an optimization component 212 receives the program216. In another embodiment, the program 216 is an object that representsa sequence of operations, including memory access operations to sourcesof data. In still another embodiment, before the program 216 is bound toa data source its access to memory is abstract. In still even anotherembodiment, once the program 216 is bound to a concrete source of data,the optimization component 212 generates a concrete program, theoptimized program 218, that uses the specific arrangement of the dataand the access pattern specified via the plurality of data types 202 a-nfor efficient access. In yet another embodiment, the optimizationcomponent 212 selects among several concrete data layouts in order toenable the most efficient concrete program, and it might select amongthese options using dynamic runtime data (for instance, the repeated useof a specific access pattern by the user). A runtime component 220executes the optimized program 218.

In some embodiments, the request is a request for an assignment of avalue to the at least one data element 210. In one of these embodiments,the request identifies an accessor 202 b and requests an assignment of avalue to the at least one data element 210. In this embodiment, a newarray node 204′ is generated with the same array source 206 as an arraynode 204 associated with the accessor 202 b. In another of theseembodiments, the request identifies a chunk 202 c and requests anassignment of a value to the at least one data element 210 associatedwith the chunk 202 c. In this embodiment, the value is copied from asource location to the at least one data element 210.

As described above, in some embodiments, an array source 206representing a copy of a data element associated with a second arraynode 204′, and representing multiple layers of access patterns, isreferred to as a proxy source 206. In one of these embodiments, therequest is for an assignment of a value to the at least one data element210 and identifies, as a source of the value, an array node 204, whichis associated with a proxy source 206. In another of these embodiments,the array node 204 is assigned to a new array source 206, which is amemory source 206′ with the same size as the period of the underlyingproxy node. In still another of these embodiments, a copy is made fromthe array node 202 a to the memory source 206′. In still even another ofthese embodiments, all nodes in a ring with which the array node 204 isassociated are set to have a default multidimensional affinetransformation. For example, all of the nodes in the ring may be set tohave a default period, offset and stride. In yet another of theseembodiments, the source array node 204 is said to have been collapsedwhen the array node 204 is associated with the memory source 206′, thecopy is made from the array node 204 to the memory source 206′, and thenodes in the array node 204 are associated with the default accesspattern. In further embodiments, the target node identified in therequest becomes a new array node 204″, which has a proxy source 206″including a reference to the source array node 204.

In still other embodiments, the request is a request to copy the atleast one data element. In one of these embodiments, a copy is made bycopying data directly to a host processor. In another of theseembodiments, a copy is made by copying data to a target processor. Instill another of these embodiments, an optimization component 212 maydetermine that a request to make a copy of the at least one data elementshould be deferred until a later, more optimal time. The optimizationcomponent 212 may make a determination as to whether and how to respondto a request to copy the at least one data element 210 responsive to oneof: an analysis of a type of first representation 206 associated withthe at least one data element 210, an analysis of a location of adestination memory and of a source memory location, an analysis of aboundary condition associated with a source memory location, and ananalysis of an access pattern associated with the at least one dataelement 210. In yet another of these embodiments, copying the at leastone data element 210 triggers an error. For example, an error may betriggered if the source and destination sizes do not match, or if aboundary condition associated with the source location does not allow areading of a requested location, or if an access pattern associated witha destination or source location force the copy to go out-of-bounds.Errors can be reported to the user by setting a flag or throwing anexception, or by some other mechanism.

In yet other embodiments, the request is a request to construct at leastone of the plurality of data types. In one of these embodiments, anarray 202 a is constructed. In another of these embodiments, theconstructed array 202 a has a given size. In still another of theseembodiments, the array 202 a is associated with physically allocatedmemory, represented by a memory source. The physically allocated memorymight reside in a number of different places, depending on the systemconfiguration; for example, in the host memory, in an acceleratormemory, or in a remote memory. In yet another of these embodiments, anarray is allocated with a specific size, although the actual allocationis deferred to a more optimal time as determined by an optimizationcomponent 212.

In another of these embodiments, the request includes an explicitinstruction to construct an accessor 202 b. In still another of theseembodiments, an accessor 202 b is constructed by an access patterngenerator function. In still even another of these embodiments, therequest includes an instruction to dereference an accessor 202 b,resulting in the construction of a chunk 202 c.

In some embodiments, a default accessor 202 b and chunk 202 c areconstructed without arguments, but are invalid. In one of theseembodiments, the default accessor 202 b and chunk 202 c are constructedwhen an array 202 a is constructed. In another of these embodiments, thedefault accessor 202 b and chunk 202 c are constructed when the array202 a is accessed. In still another of these embodiments, theinitialization of the default accessor 202 b and chunk 202 c is deferreduntil they are accessed. In yet another of these embodiments, thedefault accessor 202 b and chunk 202 c are created without arguments andare set to a state indicating that they have not yet been fullyinitialized.

In some embodiments, the optimization component 212 performs referencecounting to determine whether to maintain an array source 206 or anarray node 204. In one of these embodiments, a reference count is anumber maintained in an object that is incremented whenever a newreference to the object is created and decremented whenever a referenceis released. In another of these embodiments, a reference count of thearray source 206 results in a count of the number of rings with whichthe array source is associated. In still another of these embodiments,an array source 206 is maintained as long as it is associated with atleast one data type 202. In yet another of these embodiments, an arraynode 204 is maintained as long as it is associated with at least onedata type 202. In further embodiments, the optimization component 212may maintain references, but so might other components of the system,including the user. In some embodiments, specific optimizations can bemade if all references can be accounted for. In other embodiments,memory can be released if the reference count goes to zero; this is asimple form of “garbage collection”, also known as automatic memorymanagement.

The request is responded to with a second representation 214 of the atleast one data element 210, the second representation 214 generatedresponsive to the at least one of the plurality of data types 202 (step308). In some embodiments, the second representation 214 is an optimizedrepresentation 214 of the at least one data element 210. In one of theseembodiments, the optimized representation 214 is generated responsive toan analysis of a hardware component on which the at least one dataelement 210 resides. In another of these embodiments, the optimizedrepresentation 214 is generated responsive to an analysis of an accesspattern of the at least one data element 210. In still another of theseembodiments, the optimized representation 214 is generated responsive toan analysis of a memory layout of the at least one data element 210. Instill even another of these embodiments, the optimized representation214 is generated responsive to an analysis of the at least one dataelement 210. In yet another of these embodiments, the optimizedrepresentation 214 is generated responsive to an analysis of amodification to the at least one data element 210. In furtherembodiments, the optimized representation 214 is generated responsive toan analysis of an interaction between two data types referenced in theprogram including the request for access to the at least one dataelement 210.

In some embodiments, the request for access to the at least one dataelement includes a data type in the plurality of data types 202 havingby-reference semantics. In one of these embodiments, the data typeincluded in the request is an accessor 202 b. In another of theseembodiments, the optimization component 212 determines that the responseto the request should include a copy of the at least one data element.In still another of these embodiments, the accessor 202 b, havingby-reference semantics, returns a copy of a subset of the at least onedata element 210. In still even another of these embodiments, theoptimization component 212 determines that the response to the requestshould include a reference to the at least one data element 210. In yetanother of these embodiments, the accessor 202 b returns a pointer tothe at least one data element 210.

In some embodiments, the optimization component 212 performs theanalysis of the data element, the data types in the program, and theprogram. In one of these embodiments, the optimization component 212identifies an optimization that would improve the data access—such asdeferring a command to copy data, replacing a data type in the programwith a data type having different assignment semantics, eliminating adeferred operation which is no longer required, or generating anoptimized data structure representing the data element.

In one embodiment, the optimization component 212 determines that a datatype having a particular assignment semantic provides an optimized dataaccess. In another embodiment, the optimization component 212 generatesa second representation 214 having an assignment semantic selectedresponsive to the at least one of the plurality of data types includedin the request. In still another embodiment, the optimization component212 identifies a data type having the particular assignment semantic andproviding access to a second representation 214 of the at least one dataelement 210. In yet another embodiment, the request is responded to withthe second representation 214 provided by the identified data type. Insome embodiments, the second representation 214 is an optimized datatype providing a more efficient mechanism for accessing the dataelement. In other embodiments, the second representation 214 is anoptimized representation of the data element. In still otherembodiments, the second representation 214 represents the result ofperforming the requested computation on the data element, usingoptimized techniques selected responsive to an analysis of the requestedcomputation.

In some embodiments, the optimization component 212 returns an optimizedrepresentation of the data element 210 in response to the request. Inone of these embodiments, the optimization component 212 returns anoptimized representation of a modified version of the data element 210in response to the request. In other embodiments, the optimizationcomponent 212 returns an optimized representation of the data element210 in response to a request included in a program, the optimizedrepresentation having by-reference semantics. In one of theseembodiments, the optimized representation is an array. In another ofthese embodiments, changes to the at least one data element 210 are nolonger visible to later invocations of the program. In still otherembodiments, the optimization component 212 returns an optimizedrepresentation of the data element 210 in response to a request includedin a program, the optimized representation having by-value semantics. Inone of these embodiments, the optimized representation is an array. Inanother of these embodiments, changes to the at least one date element210 are visible to later invocations of the program. In still another ofthese embodiments, the optimized representation is a non-local variablereference. In yet other embodiments, the optimization component 212returns an optimized representation of the data element 210 in responseto a request included in a program, the optimized representation havingassignment semantics selected responsive to an analysis of a data typeincluded in the program. In one of these embodiments, optimal assignmentsemantics are selected responsive to an analysis of an interactionbetween a plurality of data types included in the program.

In some embodiments, the optimization component 212 returns theoptimized representation 214 of the data element within an optimizedversion 218 of the program 216. In one of these embodiments, theoptimization component 212 generates the optimized program 218 usingoptimized techniques selected responsive to an analysis of at least oneof the requested computation, a data type 202 included in the program216, a data structure 204, and a first representation 206. In another ofthese embodiments, the optimization component 212 provides the optimizedprogram 218 to a runtime component 220. In still another of theseembodiments, the runtime component 220 accesses the secondrepresentation 214 when executing the optimized program 218.

Referring now to FIG. 4, a block diagram depicts one embodiment of adata structure providing access to a data element, a plurality of datatypes, and a representation of the data element. As shown in FIG. 4, anarray node 204 provides access to a data element represented by arraysource 206. In one embodiment, the array node 204 specifies amultidimensional affine transformation associated with, or applied to,the at least one data element 210. In another embodiment, the array node204 specifies the access pattern—the stride, offset, andperiod—associated with the at least one data element 210. The array node204 also specifies the types with which it is associated—an array 202 a,an accessor 202 b, and a chunk 202 c. Although FIG. 4 enumerates onlythree properties of the at least one data element 210—the offset,period, and stride—it should be understood that the system may providemultiple ones of any or each of those properties or of other propertiesassociated with the at least one data element 210. Similarly, althoughFIG. 4 shows an array node 204 enumerating a period of 3, it should beunderstood that the period is a vector for the dimension of the array Nwhile offset and stride may be generalized into a N×(N+1) array forarbitrary affine transformations.

The array source 206 identifies several properties of at least one dataelement 210, including size, dimensionality, reference count, boundarymode, and operations performed on the at least one data element such ascopying, cloning, reading an element from the array, and writing a valueto an element of the array. Although FIG. 4 identifies a dimensionalityof 3, it should be understood that the at least one data element 210 maybe multidimensional and is not limited to a dimensionality of three. Thearray source 206 is associated with a proxy source 206′, a memory source206″, a grid source 206′″, and a null source 206″″. In one embodiment,the proxy source 206′ includes a pointer to the array node 204 and isassociated with a second data element represented by the array node 204.In another embodiment, a memory source 206″ represents memory that isactually allocated. In still another embodiment, the memory source 206″is a representation of undifferentiated memory that identifies in whatphysical memory data is stored. In still another embodiment, a gridsource 206′″ is a generated source 206 that returns an index of alocation as its value. In still even another embodiment, a null source206″″ represents an uninitialized source. In yet another embodiment, thenull source 206″″ indicates that an array source 206 is associated witha second node that has not been completely initialized.

The systems and methods described above may be implemented as a method,apparatus or article of manufacture using programming and/or engineeringtechniques to produce software, firmware, hardware, or any combinationthereof. The systems and methods described above may be provided as oneor more computer-readable programs embodied on or in one or morearticles of manufacture. The term “article of manufacture” as usedherein is intended to encompass code or logic accessible from andembedded in one or more computer-readable devices, firmware,programmable logic, memory devices (e.g., EEPROMs, ROMs, PROMs, RAMs,SRAMs, etc.), hardware (e.g., integrated circuit chip, FieldProgrammable Gate Array (FPGA), Application Specific Integrated Circuit(ASIC), etc.), electronic devices, a computer readable non-volatilestorage unit (e.g., CD-ROM, floppy disk, hard disk drive, etc.), a fileserver providing access to the programs via a network transmission line,wireless transmission media, signals propagating through space, radiowaves, infrared signals, etc. The article of manufacture includeshardware logic as well as software or programmable code embedded in acomputer readable medium that is executed by a processor. In general,the computer-readable programs may be implemented in any programminglanguage, LISP, PERL, C, C++, PROLOG, or any byte code language, such asJAVA. The software programs may be stored on or in one or more articlesof manufacture as object code.

Having described certain embodiments of methods and systems foroptimizing data types, it will now become apparent to one of skill inthe art that other embodiments incorporating the concepts of theinvention may be used. Therefore, the invention should not be limited tocertain embodiments, but rather should be limited only by the spirit andscope of the following claims.

1. A method for optimizing data accesses, comprising the steps of: (a)generating a data structure providing access to at least one dataelement, the data structure associated with a first representation ofthe at least one data element; (b) providing a user with a plurality ofdata types for accessing the at least one data element; (c) receiving arequest for access to the at least one data element, the requestincluding at least one of the plurality of data types; and (d)responding to the request with a second representation of the at leastone data element, the second representation generated responsive to theat least one of the plurality of data types.
 2. The method of claim 1,wherein step (a) further comprises generating a data structure providingaccess to at least one data element, the data structure associated witha first representation of the at least one data element, the firstrepresentation identifying a method for generating the at least one dataelement.
 3. The method of claim 1, further comprising the step ofgenerating the first representation of the at least one data element. 4.The method of claim 1, wherein step (a) further comprises generating adata structure providing access to at least one data element, the datastructure associated with a first representation of the at least onedata element, the first representation storing a copy of the at leastone data element.
 5. The method of claim 1, wherein step (a) furthercomprises generating a data structure providing access to at least onedata element, the data structure associated with a first representationof the at least one data element, the first representation storing aprocedurally-generated version of the at least one data element.
 6. Themethod of claim 1, wherein step (a) further comprises generating a datastructure providing access to at least one data element, the datastructure associated with a first representation of the at least onedata element, the first representation stored remotely from the at leastone data element.
 7. The method of claim 1, wherein step (a) furthercomprises generating a data structure providing access to at least onedata element, the data structure associated with a first representationof the at least one data element, the first representation stored on adisk storing the at least one data element.
 8. The method of claim 1,wherein step (a) further comprises generating a data structure providingaccess to at least one data element, the data structure associated witha first representation of the at least one data element, the at leastone data element comprising distributed data.
 9. The method of claim 1,wherein step (a) further comprises generating a data structure providingaccess to at least one data element, the data structure associated witha first representation of the at least one data element, the firstrepresentation associated with a second data structure providing accessto a second data element.
 10. The method of claim 1, wherein step (a)further comprises generating a data structure providing access to atleast one data element, the data structure associated with a firstrepresentation of the at least one data element, the firstrepresentation storing a copy of a second data element provided by asecond data structure.
 11. The method of claim 1, wherein step (a)further comprises generating a data structure providing access to atleast one data element, the data structure associated with a firstrepresentation of the at least one data element, the firstrepresentation identifying a status of an initialization process of thedata structure providing access to the at least one data element. 12.The method of claim 1, wherein step (b) further comprises providing auser with a plurality of data types for accessing the at least one dataelement, each of the data types in the plurality of data typesassociated with a data structure in a plurality of data structuresproviding access to the at least one data element.
 13. The method ofclaim 1, wherein step (b) further comprises providing a user with aplurality of data types for accessing the at least one data element,each of the data types in the plurality of data types associated withthe data structure providing access to the at least one data element.14. The method of claim 1, wherein step (b) further comprises providinga user with a plurality of data types for accessing the at least onedata element, a data type in the plurality of data types havingby-reference semantics.
 15. The method of claim 1, wherein step (b)further comprises providing a user with a plurality of data types foraccessing the at least one data element, a data type in the plurality ofdata types storing a subset of the at least one data element.
 16. Themethod of claim 1, wherein step (b) further comprises providing a userwith a plurality of data types for accessing the at least one dataelement, a data type in the plurality of data types associated with anidentification of a size of a subset of the at least one data elementassociated with the data type.
 17. The method of claim 1, wherein step(b) further comprises providing a user with a plurality of data typesfor accessing the at least one data element, a data type in theplurality of data types associated with an identification of a region ofa subset of the at least one data element associated with the data type.18. The method of claim 1, wherein step (b) further comprises providinga user with a plurality of data types for accessing the at least onedata element, a data type in the plurality of data types associated withan identification of a region of a subset of the at least one dataelement associated with the data type, the region specified by a user.19. The method of claim 1, wherein step (b) further comprises providinga user with a plurality of data types for accessing the at least onedata element, a data type in the plurality of data types associated withan identification of a stride of an array associated with the data type.20. The method of claim 1, wherein step (b) further comprises providinga user with a plurality of data types for accessing the at least onedata element, a data type in the plurality of data types associated withan identification of an offset within an array associated with the datatype.
 21. The method of claim 1, wherein step (b) further comprisesproviding a user with a plurality of data types for accessing the atleast one data element, a data type in the plurality of data typesassociated with an identification of an affine transformation.
 22. Themethod of claim 1, wherein step (b) further comprises providing a userwith a plurality of data types for accessing the at least one dataelement, a data type in the plurality of data types associated with anidentification of a non-affine transformation.
 23. The method of claim1, wherein step (b) further comprises providing a user with a pluralityof data types for accessing the at least one data element, a data typein the plurality of data types providing dereferenced access to the atleast one data element.
 24. The method of claim 1, wherein step (b)further comprises providing a user with a plurality of data types foraccessing the at least one data element, a data type in the plurality ofdata types having by-value semantics.
 25. The method of claim 1, whereinstep (b) further comprises providing a user with a plurality of datatypes for accessing the at least one data element, a data type in theplurality of data types storing a copy of the at least one data element.26. The method of claim 1, wherein step (b) further comprises providinga user with a plurality of data types for accessing the at least onedata element, a data type in the plurality of data types having aboundary condition.
 27. The method of claim 1, wherein step (c) furthercomprises receiving a request for computation of an operation on the atleast one data element, the request including at least one of theplurality of data types.
 28. The method of claim 1, wherein step (c)further comprises receiving a request for assignment of a value to theat least one data element, the request including at least one of theplurality of data types.
 29. The method of claim 1, wherein step (c)further comprises receiving a request to copy the at least one dataelement, the request including at least one of the plurality of datatypes.
 30. The method of claim 1, wherein step (c) further comprisesreceiving a request to construct at least one of the plurality of datatypes.
 31. The method of claim 1 further comprising the step ofidentifying a data type providing access to the second representation ofthe at least one data element, the data type having an assignmentsemantic selected responsive to an analysis of the at least one of theplurality of data types included in the request.
 32. The method of claim31 further comprising the step of responding to the request with thesecond representation provided by the identified type.
 33. The method ofclaim 1, wherein step (d) further comprises responding to the requestwith an optimized representation of the at least one data element, theoptimized representation generated responsive to an analysis of ahardware component on which the at least one data element resides. 34.The method of claim 1, wherein step (d) further comprises responding tothe request with an optimized representation of the at least one dataelement, the optimized representation generated responsive to ananalysis of an access pattern of the at least one data element.
 35. Themethod of claim 1, wherein step (d) further comprises responding to therequest with an optimized representation of the at least one dataelement, the optimized representation generated responsive to ananalysis of a memory layout of the at least one data element.
 36. Themethod of claim 1, wherein step (d) further comprises responding to therequest with an optimized representation of the at least one dataelement, the optimized representation generated responsive to ananalysis of the at least one data element.
 37. The method of claim 1,wherein step (d) further comprises responding to the request with anoptimized representation of the at least one data element, the optimizedrepresentation generated responsive to an analysis of a modification tothe at least one data element.
 38. The method of claim 1, wherein step(c) further comprises receiving a request for access to the at least onedata element, the request including a type in the plurality of datatypes having by-reference semantics.
 39. The method of claim 38, whereinstep (d) further comprises responding to the request with a copy of asubset of the at least one data element.
 40. The method of claim 38,wherein step (d) further comprises responding to the request with apointer to the at least one data element.
 41. A system for optimizingdata accesses comprising: a data structure providing access to at leastone data element; a first representation of the at least one dataelement associated with the data structure; a plurality of data typesfor accessing the at least one data element; and a second representationof the at least one data element, the representation generatedresponsive to at least one of the plurality of data types.
 42. Thesystem of claim 41, wherein the data structure providing access to theat least one data element is a node.
 43. The system of claim 41, whereinthe first representation of the at least one data element furthercomprises an identification of a method for generating the at least onedata element.
 44. The system of claim 41, wherein the firstrepresentation of the at least one data element further comprises a copyof the at least one data element.
 45. The system of claim 41, whereinthe first representation of the at least one data element furthercomprises a procedurally-generated version of the at least one dataelement.
 46. The system of claim 45, wherein the procedurally-generatedversion of the at least one data element comprises an array storing atleast one random number.
 47. The system of claim 45, wherein theprocedurally-generated version of the at least one data elementcomprises an array storing at least one constant.
 48. The system ofclaim 41, wherein the first representation of the at least one dataelement further comprises a representation of the at least one dataelement, the at least one data element stored remotely from the firstrepresentation.
 49. The system of claim 41, wherein the firstrepresentation of the at least one data element further comprises arepresentation of the at least one data element, the at least one dataelement stored on a disk storing the first representation.
 50. Thesystem of claim 41, wherein the first representation of the at least onedata element further comprises a representation of the at least one dataelement, the at least one data element stored on a disk identified bythe first representation.
 51. The system of claim 41, wherein the firstrepresentation of the at least one data element further comprises arepresentation of the at least one data element, the at least one dataelement comprising distributed data.
 52. The system of claim 41, whereinthe first representation of the at least one data element furthercomprises an array of indices.
 53. The system of claim 41, wherein thefirst representation of the at least one data element further comprisesa representation of an array of indices.
 54. The system of claim 41,wherein the first representation of the at least one data elementfurther comprises a representation of procedurally-generated sequence ofnumbers.
 55. The system of claim 41, wherein the first representation ofthe at least one data element further comprises a representation of anarray representing an index of a second array.
 56. The system of claim41, wherein the first representation of the at least one data elementfurther comprises an association with a second data structure providingaccess to a second data element.
 57. The system of claim 41, wherein thefirst representation of the at least one data element further comprisesa copy of a second data element provided by a second data structure. 58.The system of claim 41, wherein the first representation of the at leastone data element further comprises an identification of a representationof a second data element.
 59. The system of claim 41, wherein the firstrepresentation of the at least one data element further comprises a copyof a second data element, the second data element associated with asecond representation.
 60. The system of claim 41, wherein the firstrepresentation of the at least one data element further comprises anidentification of a status of an initialization process of the datastructure providing access to the at least one data element.
 61. Thesystem of claim 41 further comprising a plurality of data structuresproviding access to at least one data element, each data structureassociated with a data type in the plurality of data types.
 62. Thesystem of claim 61, wherein the plurality of data structures are eachassociated with a representation of the at least one data element. 63.The system of claim 61, wherein the plurality of data structurescomprise a plurality of nodes in a closed, doubly-linked list.
 64. Thesystem of claim 41, wherein the plurality of data types for accessingthe at least one data element are each associated with the datastructure providing access to the at least one data element.
 65. Thesystem of claim 41, wherein the plurality of data types for accessingthe at least one data element further comprises a data type in theplurality of data types having by-value semantics.
 66. The system ofclaim 41, wherein the plurality of data types for accessing the at leastone data element further comprises a data type in the plurality of datatypes storing a copy of the at least one data element.
 67. The system ofclaim 41, wherein the plurality of data types for accessing the at leastone data element further comprises a data type in the plurality of datatypes having a boundary condition.
 68. The system of claim 41, whereinthe plurality of data types for accessing the at least one data elementfurther comprises a data type in the plurality of data types havingby-reference semantics.
 69. The system of claim 41, wherein theplurality of data types for accessing the at least one data elementfurther comprises a data type in the plurality of data types storing asubset of the at least one data element.
 70. The system of claim 41,wherein the plurality of data types for accessing the at least one dataelement further comprises a data type in the plurality of data typesassociated with an identification of a size of a subset of the at leastone data element stored in the data type.
 71. The system of claim 41,wherein the plurality of data types for accessing the at least one dataelement further comprises a data type in the plurality of data typesassociated with an identification of a stride of an array provided bythe data type.
 72. The system of claim 41, wherein the plurality of datatypes for accessing the at least one data element further comprises adata type in the plurality of data types associated with anidentification of an offset within an array provided by the data type.73. The system of claim 41, wherein the plurality of data types foraccessing the at least one data element further comprises a data type inthe plurality of data types providing dereferenced access to the atleast one data element.
 74. The system of claim 41, wherein the secondrepresentation of the at least one data element further comprises anassignment semantic selected responsive to the at least one of theplurality of data types.
 75. The system of claim 41, wherein the secondrepresentation of the at least one data element further comprises anoptimized representation of the at least one data element generatedresponsive to an analysis of a hardware component on which the at leastone data element resides.
 76. The system of claim 41, wherein the secondrepresentation of the at least one data element further comprises anoptimized representation of the at least one data element, the optimizedrepresentation generated responsive to an analysis of the at least onedata element.
 77. The system of claim 41, wherein the secondrepresentation of the at least one data element further comprises anoptimized representation of the at least one data element, the optimizedrepresentation generated responsive to an analysis of an access patternof the at least one data element.
 78. The system of claim 41, whereinthe second representation of the at least one data element furthercomprises an optimized representation of the at least one data element,the optimized representation generated responsive to an analysis of amemory layout of the at least one data element.
 79. The system of claim41, wherein the second representation of the at least one data elementfurther comprises an optimized representation of the at least one dataelement generated responsive to an analysis of a modification to the atleast one data element.
 80. The system of claim 41, wherein the secondrepresentation of the at least one data element further comprises anoptimized representation of the at least one data element generatedresponsive to a request for assignment of a value to the at least onedata element, the request including at least one of the plurality ofdata types.
 81. The system of claim 41, wherein the secondrepresentation of the at least one data element further comprises anoptimized representation of the at least one data element generatedresponsive to a request to copy the at least one data element, therequest including at least one of the plurality of data types.
 82. Thesystem of claim 41, wherein the second representation of the at leastone data element further comprises an optimized representation of the atleast one data element generated responsive to a request to construct atleast one of the plurality of data types.